There's a
list of regulated flows in this FoI response. I haven't had a chance to look through it but this would answer the question one way or another.
If I had to guess I'd say that the "via High Wycombe" fares from the West Midlands county and beyond generally won't be regulated, but the "via Banbury" fares from Leamington will be.
Either way, fares regulation is
not the problem here since I have little doubt the DfT would give Chiltern permission to withdraw the fares if they asked. Even working within the limitations of fares regulation, Chiltern could impose much heavier time restrictions if they so desired - in line with what GWR have done for many of their regulated Super Off-Peak Returns, which only become valid from 10:30.
In any event, the sane answer to overcrowding isn't to price people off the railway. It's to provide more capacity, or (perish the thought) easing peak restrictions or offering cheaper Advance fares on quieter services to spread demand. Sadly such common sense is lacking in Britain; the only metrics used for these sorts of decisions are political and financial.